Search results for "canonical polyadic"
showing 6 items of 6 documents
Generalization of Linked Canonical Polyadic Tensor Decomposition for Group Analysis
2019
Real-world data are often linked with each other since they share some common characteristics. The mutual linking can be seen as a core driving force of group analysis. This study proposes a generalized linked canonical polyadic tensor decomposition (GLCPTD) model that is well suited to exploiting the linking nature in multi-block tensor analysis. To address GLCPTD model, an efficient algorithm based on hierarchical alternating least squa res (HALS) method is proposed, termed as GLCPTD-HALS algorithm. The proposed algorithm enables the simultaneous extraction of common components, individual components and core tensors from tensor blocks. Simulation experiments of synthetic EEG data analysi…
Shift-Invariant Canonical Polyadic Decomposition of Complex-Valued Multi-Subject fMRI Data with a Phase Sparsity Constraint
2020
Canonical polyadic decomposition (CPD) of multi-subject complex-valued fMRI data can be used to provide spatially and temporally shared components among groups with both magnitude and phase information. However, the CPD model is not well formulated due to the large subject variability in the spatial and temporal modalities, as well as the high noise level in complex-valued fMRI data. Considering that the shift-invariant CPD can model temporal variability across subjects, we propose to further impose a phase sparsity constraint on the shared spatial maps to denoise the complex-valued components and to model the inter-subject spatial variability as well. More precisely, subject-specific time …
Low-rank approximation based non-negative multi-way array decomposition on event-related potentials
2014
Non-negative tensor factorization (NTF) has been successfully applied to analyze event-related potentials (ERPs), and shown superiority in terms of capturing multi-domain features. However, the time-frequency representation of ERPs by higher-order tensors are usually large-scale, which prevents the popularity of most tensor factorization algorithms. To overcome this issue, we introduce a non-negative canonical polyadic decomposition (NCPD) based on low-rank approximation (LRA) and hierarchical alternating least square (HALS) techniques. We applied NCPD (LRAHALS and benchmark HALS) and CPD to extract multi-domain features of a visual ERP. The features and components extracted by LRAHALS NCPD…
Discovering dynamic task-modulated functional networks with specific spectral modes using MEG.
2019
Efficient neuronal communication between brain regions through oscillatory synchronization at certain frequencies is necessary for cognition. Such synchronized networks are transient and dynamic, established on the timescale of milliseconds in order to support ongoing cognitive operations. However, few studies characterizing dynamic electrophysiological brain networks have simultaneously accounted for temporal non-stationarity, spectral structure, and spatial properties. Here, we propose an analysis framework for characterizing the large-scale phase-coupling network dynamics during task performance using magnetoencephalography (MEG). We exploit the high spatiotemporal resolution of MEG to m…
Tensor decomposition of EEG signals: A brief review
2015
Electroencephalography (EEG) is one fundamental tool for functional brain imaging. EEG signals tend to be represented by a vector or a matrix to facilitate data processing and analysis with generally understood methodologies like time-series analysis, spectral analysis and matrix decomposition. Indeed, EEG signals are often naturally born with more than two modes of time and space, and they can be denoted by a multi-way array called as tensor. This review summarizes the current progress of tensor decomposition of EEG signals with three aspects. The first is about the existing modes and tensors of EEG signals. Second, two fundamental tensor decomposition models, canonical polyadic decomposit…
Multi-subject fMRI analysis via combined independent component analysis and shift-invariant canonical polyadic decomposition
2014
Canonical polyadic decomposition (CPD) may face a local optimal problem when analyzing multi-subject fMRI data with inter-subject variability. Beckmann and Smith proposed a tensor PICA approach that incorporated an independence constraint to the spatial modality by combining CPD with ICA, and alleviated the problem of inter-subject spatial map (SM) variability.This study extends tensor PICA to incorporate additional inter-subject time course (TC) variability and to connect CPD and ICA in a new way. Assuming multiple subjects share common TCs but with different time delays, we accommodate subject-dependent TC delays into the CP model based on the idea of shift-invariant CP (SCP). We use ICA …